Superfluid weight and Berezinskii–Kosterlitz–Thouless temperature of spin-imbalanced and spin–orbit-coupled Fulde–Ferrell phases in lattice systems

Abstract

We study the superfluid weight D s and Berezinskii-Kosterlitz-Thouless (BKT) transition temperatures T BKT in case of exotic Fulde-Ferrell (FF) superfluid states in lattice systems. We consider spinimbalanced systems with and without spin-orbit coupling (SOC) accompanied with in-plane Zeeman field. By applying mean-field theory, we derive general equations for D s and T BKT in the presence of SOC and the Zeeman fields for 2D Fermi-Hubbard lattice models, and apply our results to a 2D square lattice. We show that conventional spin-imbalanced FF states without SOC can be observed at finite temperatures and that FF phases are further stabilized against thermal fluctuations by introducing SOC. We also propose how topologically non-trivial SOC-induced FF phases could be identified experimentally by studying the total density profiles. Furthermore, the relative behavior of transverse and longitudinal superfluid weight components and the role of the geometric superfluid contribution are discussed.performed with quasi-one-dimensional population-imbalanced atomic gases have shown to be consistent with the existence of the FFLO state [33] but unambiguous proof is still missing.In addition to conventional spin-imbalanced quantum gas experiments, recently also synthetic SOC and Zeeman fields have been realized in ultracold gas experiments [34][35][36][37][38] which makes it possible to investigate SOC-induced FFLO states as well. As SOC-induced FFLO states have been predicted to be stable in larger parameter regime than conventional spin-imbalanced FFLO phases [10], synthetic SOC could provide a way to realize FFLO experimentally in ultracold gas systems [15].Low dimensionality has been predicted to favor 40]. However, in two and lower dimensional systems thermal phase fluctuations of the Cooper pair wave functions prevent the formation of true superfluid long range order as stated by the Mermin-Wagner theorem [41]. Instead, only quasi-long range order is possible. In two-dimensions, the phase transition from a normal Fermi gas to a superfluid state of quasi-long range order is determined by the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature T BKT [42]. Below T BKT the system is a superfluid and above T BKT superfluidity is lost.In recent years, SOC-induced FFLO phases in two-dimensional systems have gained considerable attention [7,10,13,14,20,21,25]. In these systems it has been argued that SOC accompanied with the in-plane Zeeman field would yield FFLO states. Furthermore, in [13,14] it was predicted that in the presence of the out-of-plane Zeeman field, i.e. spin-imbalance, SOC-induced FFLO states could be topologically non-trivial and support Majorana fermions. Such topological FFLO states are conceptually new and exotic superconductive phases of matter. However, these studies were performed by applying mean-field theories which do not consider the stability of FFLO states against thermal phase fluctuations in terms of the BKT transition. Superfluidity and BKT transition temperatures of BCS phases in spin-...

Mean-field theory for superconductivity in twisted bilayer graphene

“…Therefore, the mean-field T c gives an upper bound for the measured transition temperature. Furthermore, even the BKT transition temperature can be calculated from the mean-field superfluid weight [44]. The mean-field results are also relevant in that the (L)DOS can be experimentally measured by tunneling experiments and this depends on the structure and magnitude of mean-field ∆ at temperatures below the BKT transition.…”

Quantum-geometric perspective on spin-orbit-coupled Bose superfluids

“…( 26) can also be split into two parts, ρ i j = ρ intra i j + ρ inter i j , depending on the physical origin of the terms [11,12]: the intraband (interband) processes give rise to the conventional (geometric) contribution. This division is motivated by the success of a similar description with Fermi SFs [3,7].…”

“…The physical mechanism is quite clear in a multiband lattice: the geometric effects originate from the dressing of the effective mass of the SF carriers by the interband processes, which in return controls those SF properties that depend on the carrier mass. Besides the SF density and weight, the list includes the velocity of the low-energy Goldstone modes and the critical Berezinskii-Kosterlitz-Thouless temperature [1][2][3][4][5][6][7][8]. On the other hand, the intraband processes give rise to the conventional effects.…”

“…Motivated by the success of analogous works on spinorbit-coupled Fermi SFs [3][4][5]7], here we investigate the SF properties of a spin-orbit-coupled Bose gas from a quantumgeometric perspective. Our work differs from the existing literature in several ways [15][16][17].…”